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Elementary-number-theory
New post in Elementary-number-theory
$a/b\bmod{m}$ when $m$ is not a prime
June 7th, 2022
elementary-number-theory
modular-arithmetic
$3^{15} \mod 17$ I would like using Fermat theorem and doing something like this $\frac{3^{16}}{3} \mod 17$ that is possible?
June 8th, 2022
modular-arithmetic
elementary-number-theory
Find all positive integers $n$ such that $n^4 − 1$ is divisible by 5.
June 8th, 2022
modular-arithmetic
elementary-number-theory
divisibility
When a prime number p divides $ab$ then we have either p divides a or p divides b.Prove that $\sqrt {p} $ is not rational for any prime number p.
June 8th, 2022
irrational-numbers
elementary-number-theory
prime-numbers
Is this the general solution of finding the two original squares that add up to a given integer N?
June 8th, 2022
sums-of-squares
elementary-number-theory
Show that: $97\mid (2^{48})-1$
June 8th, 2022
elementary-number-theory
Greatest Common Divisor of prime numbers
June 8th, 2022
gcd-and-lcm
elementary-number-theory
Prove that $n^2 + 1$ is not a multiple of $6$ for any positive integer $n$
June 8th, 2022
elementary-number-theory
modular-arithmetic
$x^4 = -1$ (mod $p$) implies p = 1 mod 8
December 17th, 2020
number-theory
prime-numbers
elementary-number-theory
Find the pairs $(x,y) ; 0 \le x,y \le 18$ such that $19 \vert 3x+4y+5$
June 8th, 2022
divisibility
elementary-number-theory
number-theory
Finding last two non-zero digits of 2016!
June 8th, 2022
factorial
elementary-number-theory
If $\gcd(a,b) = 1$, show that $\gcd(2a+b, a+2b)=1 \mbox{ or } 3$
June 8th, 2022
elementary-number-theory
arithmetic
Solve the following congruence: 2x ≡ 7 (mod 17)
June 8th, 2022
elementary-number-theory
discrete-mathematics
modular-arithmetic
Number theory question from today's Pre - RMO
June 8th, 2022
divisibility
elementary-number-theory
Proof by induction with a prime number
June 8th, 2022
elementary-number-theory
induction
Are all numbers rational?
June 8th, 2022
elementary-number-theory
definition
rational-numbers
irrational-numbers
How can I solve $4x + 51y = 9$ using congruences?
June 6th, 2022
congruences
elementary-number-theory
modular-arithmetic
how to prove that $n(n+1)$ can't be square?
June 8th, 2022
elementary-number-theory
How to solve $ x^2+4x+2 \equiv 0 \pmod{49}$
June 8th, 2022
diophantine-equations
elementary-number-theory
modular-arithmetic
Suppose a, b and n are positive integers. Prove that (a^n) | (b^n) if and only if a | b.
November 19th, 2020
divisibility
elementary-number-theory
Extension of Fermat's little theorem with Carmichael numbers
June 8th, 2022
prime-numbers
cryptography
elementary-number-theory
difference between 2 prime numbers
June 8th, 2022
number-theory
elementary-number-theory
Formula For Finding the Next Near Consecutive Perfect Square
August 7th, 2020
algebra-precalculus
elementary-number-theory
terminology
A number relatively prime to n in the integers mod n produces all the elements
June 8th, 2022
elementary-number-theory
Show that $51| 10^{32n+9} - 7$
November 11th, 2020
elementary-number-theory
The product of any two even integers is a multiple of 4
June 8th, 2022
elementary-number-theory
How many coprime ordered pairs are there up to $N$?
June 8th, 2022
probability-theory
combinatorics
elementary-number-theory
totient-function
Let m and n be positive integers with (m,n) = 1. Prove that each divisor d > 0 of m*n can be written uniquely
June 8th, 2022
elementary-number-theory
number-theory
Show that the square of any odd positive integer is of the type 6q or 6q+ 3 or 6q + 5 where q is some integer
June 4th, 2020
modular-arithmetic
elementary-number-theory
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
March 5th, 2020
elementary-number-theory
proof-writing
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