List questions from congruences

Published on 16 Apr 2026 - 0:38

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Proof that any square is of the form $3k$ or $3k+1$

Published on 15 Apr 2026 - 21:56

1.8k

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Does a solution exist where $p,q$ are odd primes and $p^a - q^b = p^c - q^d$ where $a > c > 1$ and $b > d > 1$

Published on 17 Apr 2026 - 9:03

677

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Proving congruence $24^{31}\equiv 23^{32}\pmod {19}$

Published on 15 Apr 2026 - 16:39

1.3k

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Subset of prime numbers

Published on 14 Apr 2026 - 22:47

2.4k

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Solving mod congruence

Published on 11 May 2026 - 1:48

81

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Proving that if $a,b > 1$, then $5^a - 3^b=16$ has only one solution with $a=2$ and $b=2$

Published on 16 Apr 2026 - 15:16

74

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Solve for $p^a + 1 = 2\cdot q^b$ where $p,q$ are odd primes and $a,b \ge 2$

Published on 17 Apr 2026 - 3:00

41

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Find all solutions to $x^3-x^2+2x-2=0 \pmod {11}$

Published on 17 Apr 2026 - 13:53

53

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Need help in understanding $ord_p{a}$ as used in Theorem 1.1 from "On Some Exponential Equations Of S. S. Pillai"

Published on 15 Apr 2026 - 13:16

5.3k

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Determine the last two digits of $3^{3^{100}}$

Published on 12 Apr 2026 - 18:27

705

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Finding $7$ inverse modulo $11$

Published on 16 Apr 2026 - 0:40

83

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Confused by a step in a proof that $a^x - b^y = c$ has at most two solutions in positive integers $x,y$

Published on 12 Apr 2026 - 1:17

2.2k

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Find an integer $x$ satisfying the congruence:

Published on 15 Apr 2026 - 20:13

361

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Find all solutions to this system of congruences

Published on 14 Apr 2026 - 18:51

List Question

Find the smallest positive integer x such that 2015! ≡ x (mod 2017)

Proof that any square is of the form $3k$ or $3k+1$

Does a solution exist where $p,q$ are odd primes and $p^a - q^b = p^c - q^d$ where $a > c > 1$ and $b > d > 1$

Proving congruence $24^{31}\equiv 23^{32}\pmod {19}$

Subset of prime numbers

Solving mod congruence

Proving that if $a,b > 1$, then $5^a - 3^b=16$ has only one solution with $a=2$ and $b=2$

Solve for $p^a + 1 = 2\cdot q^b$ where $p,q$ are odd primes and $a,b \ge 2$

Find all solutions to $x^3-x^2+2x-2=0 \pmod {11}$

Need help in understanding $ord_p{a}$ as used in Theorem 1.1 from "On Some Exponential Equations Of S. S. Pillai"

Determine the last two digits of $3^{3^{100}}$

Finding $7$ inverse modulo $11$

Confused by a step in a proof that $a^x - b^y = c$ has at most two solutions in positive integers $x,y$

Find an integer $x$ satisfying the congruence:

Find all solutions to this system of congruences

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