TMUA Official 2019 Paper 2 · Question 7

For which one of the following statements can the fact that $12^2+16^2=20^2$ be used to produce a counterexample?

AIf

a

b

and

c

are positive integers which satisfy the equation

a^2+b^2=c^2

, and the three numbers have no common divisor, then two of them are odd and the other is even.

BThe equation

a^4+b^2=c^2

has no solutions for which

a

b

and

c

are positive integers.

CThe equation

a^4+b^4=c^4

has no solutions for which

a

b

and

c

are positive integers.

DIf

a

b

and

c

are positive integers which satisfy the equation

a^2+b^2=c^2

, then one is the arithmetic mean of the other two.

examday