user587054

### Questions (35)

 7 Prove that if $a, b, c \in \mathbb{Z^+}$ and $a^2+b^2=c^2$ then ${1\over2}(c-a)(c-b)$ is a perfect square. 6 If $a,b,c,d\in\mathbb{Z^+}$ where $ad=b^2+bc+c^2$, prove that $a^2+b^2+c^2+d^2$ is composite 6 If $a+b=1$ find the greatest value for $a^2b^3$ 6 Prove that $q^i \equiv 1 \pmod {n!}$ for all $q, n \in \mathbb{Z^+}$ where the prime factors of $q$ are greater than $n$ 5 Prove that for all $n\ge2\in\mathbb{Z}$ and $p$ is prime then $n^{p^p}+p^p$ is composite.

### Reputation (617)

 +10 If a, b belong to S prove that ab belongs to S +20 Find all positive integers $n$ and $m$ such that $(125\times2^n)-3^m=271$ +16 Find the value of $S$ if $S = {x\over y} + {y\over z} + {z\over x} = {y\over x} + {z\over y} + {x\over z}$ and $x + y + z = 0$ +5 If $a,b,c,d\in\mathbb{Z^+}$ where $ad=b^2+bc+c^2$, prove that $a^2+b^2+c^2+d^2$ is composite

 3 How can you simplify $\sqrt{9-6\sqrt{2}}$? 2 Prove $\gcd(n,n+2)=1$ if $n$ is odd and $2$ if $n$ is even

### Tags (22)

 3 radicals 0 factorial × 2 2 elementary-number-theory × 19 0 substitution × 2 2 greatest-common-divisor 0 fractions × 2 0 algebra-precalculus × 16 0 a.m.-g.m.-inequality × 2 0 inequality × 3 0 combinatorics × 2

### Accounts (3)

 Mathematics 617 rep 11 Chemistry 101 rep Super User 58 rep 6