IMO 1974 LL YUG50

Let m and n be natural numbers with m > n. Prove that

imolonglistmathematicsolympiad

IMO 1974 LL YUG50

Origin: YUG

Problem

Let m and n be natural numbers with m > n. Prove that 2(m −n)2(m2 −n2 + 1) \geq2m2 −2mn + 1.