1

Part of 1999 May Olympiad

Problems(2)

numbers equal to the sum of the cubes of its digits

Source: V May Olympiad (Olimpiada de Mayo) 1999 L2 P1

A three-digit natural number is called tricubic if it is equal to the sum of the cubes of its digits. Find all pairs of consecutive numbers such that both are tricubic.

number theoryDigits

ways to choose 2 numbers with product multiple of 5 and difference 5

Source: V May Olympiad (Olimpiada de Mayo) 1999 L1 P1

Two integers between

1

100

inclusive are chosen such that their difference is

7

and their product is a multiple of

5

. In how many ways can this choice be made?

number theoryalgebra