Let $a , b , c \in \mathbb { N }$ be such that $$a ^ { 2 } + b ^ { 2 } = c ^ { 2 } \text { and } c - b = 1$$ Prove that ( i ) $a$ is odd, ( ii ) $b$ is divisible by 4 , (iii) $a ^ { b } + b ^ { a }$ is divisible by $c$.
Let $a , b , c \in \mathbb { N }$ be such that
$$a ^ { 2 } + b ^ { 2 } = c ^ { 2 } \text { and } c - b = 1$$
Prove that\\
( i ) $a$ is odd,\\
( ii ) $b$ is divisible by 4 ,\\
(iii) $a ^ { b } + b ^ { a }$ is divisible by $c$.