What is the smallest positive integer that cannot be expressed as the sum of at most 19 cubes of positive integers?

The average (arithmetic mean) of three different positive integers is 13. If the second integer is 4 times as large as the third integer, what is the smallest possible sum of the first and the third integers? a. 7 b. 8 c. 9 d. 11

11.) LCM and GCD. The least common multiple of nonzero integers a and b is the smallest positive integer m such that a | m and b |m; m is usually denoted (a, b]. Prove that (a) Whenever a | k and b | k, then [a, b] | k; (btria, b]- ab/(a, b) if a 0 and b >0. qcd(a, b)

What is the units digit of y? a. 3 b. 2 c. 1 d. 0 The average (arithmetic mean) of three different positive integers is 15. If the first integer is 10 times as large as the second integer, what is the smallest value of the third integer? a. 4 b. 3 c 2 d. 1. The average (arithmetic mean) of