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Keith Backman
  • Member for 10 years, 3 months
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34 votes

Can any number of squares sum to a square?

7 votes
Accepted

Find all positive integers $n$ such that $36^n - 6$ is the product of three consecutive naturals.

7 votes
Accepted

Show that there are infinitely many natural numbers such that $a^2+b^2=c^2+3 .$

7 votes

How To solve This Perfect Square Word Problem

7 votes

Why does fermat little theorem work?

6 votes

Proving true or false integral solution to equation $X^2-13Y^2 = 7$

6 votes

Does digit $6$ always lead to $\ 25921=161^2\ $?

6 votes

Does it follow from Gödel's theorem that this world cannot be fully described by math?

5 votes

Why are even primes notable?

5 votes
Accepted

What is the number of different sums of the items of a set of consecutive natural numbers?

5 votes
Accepted

Are there any 2 primitive pythagorean triples who share a common leg?

5 votes
Accepted

$x$, $y$, $z$ are distinct non-zero digits such that $zyx+zyx+zyx=xxx$ (concatenation, not multiplication) ...

4 votes

What is notable about the composite numbers between twin primes?

4 votes
Accepted

The product of which 6 primes is 201-times larger than their sum?

4 votes

How many five-digit positive integers are there that are divisible by three?

4 votes

does a number that contains all primes less than it exist?

4 votes

Prove that the product of any two numbers between two consecutive squares is never a perfect square

4 votes
Accepted

Iterating sum of squares of decimal digits of an integer : how big can it grow?

4 votes

Suppose $p$ and $p-2$ are both prime numbers where $p>5$. Prove $6$ divides $p-1$.

3 votes

There exist infinitely many prime numbers $p≥2$ and there exist positive integers $k,m$ such that $k^2+1=p+m$

3 votes

For how many integers $n$ is $n^6+n^4+1$ a perfect square?

3 votes

Solve $a_1^2 + 2a_2^2 + 3a_3^2 + ... + na_n^2 = a_{n+1}^2$ for natural numbers

3 votes
Accepted

Cubes as the sum of odd integers

3 votes

If $p^2-n^2$ is divisible $12$, where $p$ is prime, does that mean that $n$ is a prime?

3 votes
Accepted

Positive integer $n$ is divisible by a cube, if it has three prime divisors and at least seven divisors $p^k$ ($p$ prime and $k$ positive integer).

3 votes
Accepted

Is there any perfect square number can write in $p\cdot q\cdot r-p-q-r$? where $p,q,r $ are odd primes.

3 votes
Accepted

Sum of Prime Factorizations and Primes

3 votes

Given $z^2-1\mid x^2z^2-1$, prove $\frac{x^2z^2-1}{z^2-1}$ is never prime, for $x$, $z$ integers such that $x>z>1$.

3 votes

Dealt 3 cards. Odds of being dealt any pair?

3 votes
Accepted

Let $m,n$ be positive integrars such that $\gcd(m,n) = 6$ find $\operatorname{lcm(}4m,21n)$?

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