Question

For all integral values of n the expression ((7^2n)-(3^3n)) is a multiple of

Answer 1

${7}^{2x} - {3}^{3x}$
Now 7 is an odd number, and an odd number raised to an integer power is always odd.
This means that both (7^2x) and (3^3x) will be odd.
And we know that the difference of 2odd numbers is always even and every even number is a multiple of 2.
Thus
${7}^{2x} - {3}^{3x} \: \: \: \: is \: always \: divisible \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: by \: 2$