Question

Find two pairs of solutions for a and b, such that, a^b +b^a=100, where a and b are natural numbers

Answer 1

it can be solved with help of ' hit and trail method' .

if we choose a = 1 and b = 99
then,
a^b + b^a = 1^99 + 99^1 = 1 + 99 = 100

and if we choose
a = 2 and b = 6
a^b + b^a = 2^6 + 6^2 = 64 + 36 = 100

hence, two pair of solutions are ( 1, 99) , (2, 6)
or, (99, 1) and ( 6, 2)