26th Putnam 1965 Problem A1 How many positive integers divide at least one of 10 40 and 20 30 ? Solution
: 2301. Factors of 10 40 have the form 2 m 5 n with 0 <= m, n <= 40. So there are 41 2 = 1681 such factors. Factors of 20 30 = 2 60 5 30 not dividing 10 40 have the form 2 m 5 n with 41 ≤ m ≤ 60 and 0 ≤ n ≤ 30, so there are 20.31 = 620 such factors. 4th Putnam 1941 © John Scholes jscholes@kalva.demon.co.uk 3 Nov 1999