tmua.me Medium Set C Paper 2 · Question 19

The positive integers $a$ and $b$ have highest common factor $1$ . Both $ab$ and $a+b$ are perfect squares.

Which of the following statements must be true?

\begin{array}{ll} \text{I}&a\text{ and }b\text{ are both perfect squares.}\\[3pt] \text{II}&a+b\text{ is odd.}\\[3pt] \text{III}&\text{At least one of }a,b\text{ is divisible by }5. \end{array}

ANone of them

BI only

CII only

DIII only

EI and III only

FI and II only

GII and III only

HI, II and III

examday