Question 54
A sequence of numbers is called complete if its terms are positive integers and every positive integer has at least one multiple among its terms.
Prove that an arithmetic progression is a complete sequence if and only if its common difference divides its first term.
Problem (second source-language version):
A sequence of numbers is called complete if its elements are nonzero natural numbers and every nonzero natural number has at least one multiple that is a term of the sequence.
Prove that an arithmetic progression is complete if and only if its common difference divides its first element!
Prove that an arithmetic progression is a complete sequence if and only if its common difference divides its first term.
Problem (second source-language version):
A sequence of numbers is called complete if its elements are nonzero natural numbers and every nonzero natural number has at least one multiple that is a term of the sequence.
Prove that an arithmetic progression is complete if and only if its common difference divides its first element!