List questions from elementary-number-theory

Published on 12 Apr 2026 - 10:29

77

Views

For what non trivial values of $a$ and $k$, $a^k + 1$ will be prime?

Published on 14 Apr 2026 - 1:37

1.5k

Views

What is the maximum value of (a + k b) mod M?

Published on 13 Apr 2026 - 18:27

1k

Views

Irreducibility using Fermat's Little Theorem

Published on 11 Apr 2026 - 13:21

71

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Solve $1+a^c+b^c=\text{lcm}(a^c,b^c)$

Published on 09 Apr 2026 - 1:49

575

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Solve $abc+bcd+cda+dab=abcd+3$ in $\mathbb{N}$.

Published on 25 Mar 2026 - 17:36

52

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Is $\sum_{i=0}^{a-1}\binom{a}{i}\binom{2a-i}{a} $ even?

Published on 11 Apr 2026 - 22:34

826

Views

Quadratic Residues Proof

Published on 06 Apr 2026 - 20:59

2.8k

Views

If $P$ is a polynomial with $P(3)=10$ and $P(1)=1$, then why can't all the coefficients of $P$ be integers?

Published on 29 Mar 2026 - 20:06

47

Views

Proof by divisibility. Should I choose $a=p$ and $b=p^2$?

Published on 25 Mar 2026 - 8:09

97

Views

How to show that that $q \mid p-1$?

Published on 13 Apr 2026 - 21:10

77

Views

Is there such natural number N, such that a^c has 10 distinct digits, for natural a and c >= N?

Published on 20 Mar 2018 - 15:30

304

Views

Is $x^5+x+5=y^2$ solvable over the integers?

Published on 25 Mar 2026 - 17:38

165

Views

A polynomial problem, Source: AOPS

Published on 12 Apr 2026 - 5:16

60

Views

Find the order of each element.

Published on 20 Mar 2018 - 19:35

List Question

A problem from a mathematical olympiad

For what non trivial values of $a$ and $k$, $a^k + 1$ will be prime?

What is the maximum value of (a + k b) mod M?

Irreducibility using Fermat's Little Theorem

Solve $1+a^c+b^c=\text{lcm}(a^c,b^c)$

Solve $abc+bcd+cda+dab=abcd+3$ in $\mathbb{N}$.

Is $\sum_{i=0}^{a-1}\binom{a}{i}\binom{2a-i}{a} $ even?

Quadratic Residues Proof

If $P$ is a polynomial with $P(3)=10$ and $P(1)=1$, then why can't all the coefficients of $P$ be integers?

Proof by divisibility. Should I choose $a=p$ and $b=p^2$?

How to show that that $q \mid p-1$?

Is there such natural number N, such that a^c has 10 distinct digits, for natural a and c >= N?

Is $x^5+x+5=y^2$ solvable over the integers?

A polynomial problem, Source: AOPS

Find the order of each element.

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