Suppose $a,b$ are integers. If $4\mid(a^2 +b^2)$, then $a$ and $b$ are not both odd.
35052
Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
134765
Is an integer a sum of two rational squares iff it is a sum of two integer squares?
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
18953
Prove that even + odd is odd.
2771
A group has odd number of elements iff each element is a square, $a=b^2$.
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]