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Number-theory
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Representing a given number as the sum of two squares.
August 1st, 2022
number-theory
sums-of-squares
Prove that $(3n)!/(3!)^n$ is an integer
August 1st, 2022
number-theory
Prove that there is some positive integer $n$ such that $n, n +1, n+2,... , n + 200$ are all composite.
August 1st, 2022
number-theory
Missing Exercises in Elementary Number Theory by Underwood Dudley.
August 1st, 2022
number-theory
elementary-number-theory
reference-request
online-resources
Prove that for any integer $k \ne 0$, $\gcd(k, k+1) = 1$
July 10th, 2021
number-theory
elementary-number-theory
gcd-and-lcm
Let $F_n$ denote the nth Fibonacci number and prove that the following re true for every possible integer $n$
February 1st, 2020
number-theory
discrete-mathematics
fibonacci-numbers
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
October 26th, 2020
number-theory
divisibility
gcd-and-lcm
Square-Trangular Numbers Checking Answer
May 19th, 2020
number-theory
Difference between surjections, injections and bijections
January 12th, 2020
combinatorics
functions
discrete-mathematics
number-theory
Why $\mathbb{Z}[\sqrt{-3}]$ is not a Euclidean domain?
November 13th, 2020
ring-theory
abstract-algebra
number-theory
Prove $2$ is only even prime
August 1st, 2022
number-theory
What is the remainder when $40!$ is divided by $1763$?
January 1st, 2020
number-theory
chinese-remainder-theorem
factorial
How to get the ceiling function and floor function value of $\frac{2+4\sqrt{3}}{5}$?
February 10th, 2020
number-theory
$ax^2+bx+c \equiv 0 \pmod p$ has solution iff $p \mid b^2-4ac$ or $b^2-4ac$ is a quadratic residue $\mod p$
June 23rd, 2020
number-theory
If p is a prime number of the form $4n+3$, show that we cannot solve $x^2\equiv -1\mod p$
August 1st, 2022
abstract-algebra
group-theory
number-theory
finite-groups
solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$
June 24th, 2020
number-theory
congruences
modular-arithmetic
elementary-number-theory
quadratic-residues
Calculating $\phi(63)$
May 26th, 2020
elementary-number-theory
number-theory
totient-function
If 'a' is a natural number and 'b' is a digit such that $(3a+2007)^2=4b85924$, then find $a-b$.
August 1st, 2022
elementary-number-theory
number-theory
Extract each digit of a number
November 14th, 2020
number-theory
Proving the product of four consecutive odd integers is always 16 less than a square number.
February 3rd, 2020
number-theory
integral solution of n such that [nC10][(n+1)C10] is a perfect square?
August 1st, 2022
number-theory
combinatorics
combinations
Is the set of all prime numbers bounded?
August 1st, 2022
number-theory
prime-numbers
elementary-set-theory
Find the remainder when a number is divided by 999 given the following conditions
June 27th, 2020
number-theory
What is the possible relation between the twin prime conjecture and the Goldbach's conjecture
August 15th, 2020
prime-numbers
number-theory
finding the greatest perfect square dividing an integer
March 29th, 2020
prime-numbers
number-theory
Proving two consecutive odd primes have at least 3 prime divisors.
August 1st, 2022
number-theory
Is $\underbrace{11111\ldots1}_{91\text{ times}}$ a prime number?
August 1st, 2022
number-theory
prime-numbers
repunit-numbers
Prove that (integer + non-integer) never equals an integer.
August 1st, 2022
proof-writing
algebra-precalculus
number-theory
best approximation of $\sqrt{2}$
August 1st, 2022
irrational-numbers
approximation-theory
number-theory
approximation
Find the remainder when $1!$+$2!$+$3!$....$49!$ is divided by 7?
November 3rd, 2020
number-theory
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