1. Does the equation $x^2+x=a$ have an integer solution?
  2. Diophantine equation $x^p+ax=y^p+by$

  3. Have there been any updates on Mochizuki's proposed proof of the abc conjecture?
  4. Feit-Thompson conjecture
  5. Examples of groups that play an important role in Arithmetic geometry?

  6. Parity of number of primes

  7. Writing integers as determinants of matrices with prime entries.
  8. Is there always one integer between these two rational numbers?

  9. Difference of Beilinson conjecture and equivariant Tamagawa number conjecture

  10. A problem involving the inverse Collatz map
  11. Finding short linear combinations in abelian groups

  12. A property of 47 with respect to partitions into five parts
  13. Does a $K_{\upsilon}$-point of a variety $V$ give a point of $V$ in $K_{(\upsilon)}=K^{sep}\cap K_{\upsilon}$ for a global field $K$?

  14. Approximating the sum $\sum_{n \leq X} a_n$ with a smooth sum $\sum_{n \geq 1} a_n w(X)$

  15. Understanding Vaughan's Identity
  16. How small can intervals be and still contain a prime times a power of 2?

  17. Is there always at least one prime in the closed interval $[2^n,2^n+n^2]$?
  18. Improving prime number generation probability?

  19. parity of index of subgroup of unit group generated by a Minkowski unit and its conjugates
  20. A special kind of multiplicative function $f: \mathbb N \to \mathbb N$ such that $f(p)=p+k$ for all odd prime $p$, where $k>1$ is a fixed odd integer
  21. Number field analog of Artin-Tate $\Rightarrow$ BSD?
  22. Question about the term $\sum_{ \rho} \frac{X^{\rho}}{\rho}$ in the explicit formula of $\sum_{n \leq X} \Lambda(n) \chi(n)$

  23. Reference for explicit formula for $\sum_n \Lambda(n) \chi(n)$ with smooth weights
  24. Can the relative degree and ramification index can be read off the characteristic polynomial?
  25. Why could Mertens not prove the prime number theorem?

  26. Q re Kaprekar's fixed mapping points
  27. Chern Classes or Chern character classes in the Lichtenbaum-Quillen conjecture?
  28. A quote by Lev Landau about prime numbers

  29. What is the solution, $f(n)$, of the following functional equation: $mf(m)+nf(n)=(m+n+xmn)f(m+n+xmn)$?

  30. periods of higher weight modular forms

  31. For which values of $k$ is it known that there are infinitely many $n$, such that $2^{n+k}\equiv 1\pmod{n}$?

  32. Volumes of Hecke operators

  33. How to bound $\sum_{1 \leq x_1, ..., x_n \leq N} lcm(x_1, ..., x_n)^{- \delta}$?
  34. Lower bounds for the top rational cohomology of arithmetic groups

  35. Question re the Fano plane ordered triples and non-commutatively paired binomial integer decompositions (allowing 0)
  36. Unprovable integer identity involving exponentiation

  37. Arithmetic geometry examples

  38. Finding index/period of a semigroup element
  39. Question about theorem related to FLT, first case

  40. some phenomena about Fibonacci number

  41. Pythagorean 5-tuples
  42. Expression of the root number for Maass forms
  43. Primes representable as difference of two integer powers with different exponents
  44. Why linearization leads to arithmetization?

  45. Short divisor sum
  46. Infinite subset of $\mathbb{N}$ almost avoiding all "zebra crossings"
  47. If $N = qn^2$ is an odd perfect number, is it possible to have $q + 1 = \sigma(n)$?
  48. 180 = (4*14) + (4*15) + (4*16) in relation to OEIS A005555 (a finite sequence associated with the Lie algebra $E_8$.)
  49. Building sequences with the help of sum-of-digits function and concatenation and occurence of primes in them
  50. Chow Groups of varieties over number fields
  51. 40 = (4*1) + (4*2) + (4*7) in relation to OEIS A075308
  52. Error term for Vinogradov's three prime theorem
  53. On a permanent related rank?

  54. On generating squarefree integers and primes?

  55. Relaxed Collatz 3x+1 conjecture
  56. Conjecture on Odd Perfect Numbers
  57. Name of the sum of the $k$-wise product of distinct integers from $1$ to $n$

  58. Binary weight of shifted integers

  59. Name of amateur who gave a new proof of the Ramanujan-Nagell theorem?
  60. Elements of absolute value 1 in cyclotomic extension of dyadic rationals
  61. How to show that the following function isn't a polynomial over Q?
  62. Estimate for de Bruijn function with small fixed smoothness bound
  63. Is the following function a polynomial?
  64. (Variation of an old question) Are these functions polynomials?
  65. Finding binary quadratic forms which parametrize a conic
  66. "Super" multinomial coefficients
  67. Asymptotic formula, polynomial, irrational number and uniformly distribution

  68. Kottwitz's vertical map
  69. From prime to prime by squaring the digits
  70. Is there an $n\ge1$ such that every prime $p\equiv1\pmod{9}$ is representable in the form $x^2+ny^2$?
  71. A general question about strictly non-palindromic numbers

  72. Simple proof for $\sum_{i=1}^n a^{\gcd(i,n)} $ is divisible by $n$
  73. Normalizing trains without sign walking in compartments

  74. Torsion of an abelian variety under reduction.

  75. If $q^k n^2$ is an odd perfect number with Euler prime $q$, is $\sigma(q^k)/n + \sigma(n)/q^k$ bounded from above?

  76. Open problems in continued fractions theory

  77. Are all zeros of $\dfrac{\Gamma'}{\Gamma^2}(s) \pm \dfrac{\Gamma'}{\Gamma^2}(1-s)$ either real or on the line with $\Re(s)=\frac12$?
  78. About transfer from Hilbert modular forms to Siegel modular forms

  79. A counting problem related to twin primes
  80. Is every square root of an integer a linear combination of cosines of $\pi$-rational angles?
  81. When can a 'polynomial' have an infinite number of zeroes
  82. On the consistency of the definition of the conductor for automorphic forms
  83. Inverse to a Diophantine number

  84. Algorithm to compute Discriminant of an $n$ element set over a number field

  85. What is wrong with this modification of the definition of Shimura datum?

  86. Poles of $L$-functions associated to Maass forms

  87. About the validity of a new conjecture about a diophantine equation
  88. Norm to Principal Ideal

  89. Diophantine approximation of algebraic number
  90. Primes of the form $4x+1$

  91. Example of two p-Ordinary Elliptic Curves congruent to each other

  92. Can Davenport's estimate be extended to cubic polynomials with non-zero discriminant?

  93. Existence of certain cubes in finite fields

  94. Automorphisms in function fields with $\mathbb F_q[T]$ globally invariant

  95. Examples of automorphic forms over $\mathbb{H}^3/\text{PSL}_2(\mathbb{Z}[i])$

  96. Can a number be palindromic in more than 3 consecutive number bases?

  97. Primality test similar to the AKS test

  98. For which Functions is the (generalized) Riemann hypothesis known?

  99. A trace formula for $\mathrm{GSp(4)}$
  100. Relation between Hecke operators and coefficient of L-functions