MathDB

about four integers

Source:

May 12, 2010

Putnamnumber theory unsolvednumber theory

Problem Statement

a, b, c, d

are positive integers, and

r=1-\frac{a}{b}-\frac{c}{d}

.
And,

a+c \le 1982, r \ge 0

. Prove that

r>\frac{1}{1983^3}