8

Part of 2013 NZMOC Camp Selection Problems

Problems(1)

c = a + b/a -1/b is perfect square.

Source: New Zealand NZMOC Camp Selection Problems 2013 p8

a

b

are positive integers such that

c = a +\frac{b}{a} -\frac{1}{b}

is an integer. Prove that

c

is a perfect square.

Perfect Squarenumber theory