(1 point) prove the following statement: if a e z and n e n, then gcd(a, a + n)|n. proof: let gcd(a, a n) = d. this implies that and therefore for some y e z. for some x e z and e z. therefore since x, y e z, therefore thus n= о. е. d.

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. which of these statements are true? check all that apply. there are 20c3 possible ways to choose three books to read. there are 5c3 possible ways to choose three mysteries to read. there are 15c3 possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as . the probability that mariah will not choose all mysteries can be expressed as 1 −