MathDB

A5

Part of 1982 Putnam

Problems(1)

about four integers

Source:

5/12/2010
a,b,c,da, b, c, d are positive integers, and r=1−ab−cdr=1-\frac{a}{b}-\frac{c}{d}.
And, a+c≤1982,r≥0a+c \le 1982, r \ge 0. Prove that r>119833r>\frac{1}{1983^3}.
Putnamnumber theory unsolvednumber theory