MathDB

4

Part of 1959 Poland - Second Round

Problems(1)

a_n =3(n^2 + n) + 7 , NT

Source: Polish MO second round 1959 p4

8/29/2024
Given a sequence of numbers 13,25,43,… 13, 25, 43, \ldots whose n n -th term is defined by the formula an=3(n2+n)+7a_n =3(n^2 + n) + 7 Prove that this sequence has the following properties:
1) Of every five consecutive terms of the sequence, exactly one is divisible by 5 5 ,
2( No term of the sequence is the cube of an integer.
number theoryperfect cubedivides