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Found: 22

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Sequences Recurrent relations Linear recurrent relations Calculus Number sequences Number sequences (other)

13–15 3.0

The sequence of numbers \(a_1, a_2, \dots\) is given by the conditions \(a_1 = 1\), \(a_2 = 143\) and

for all \(n \geq 2\).

Prove that all members of the sequence are integers.

Problem #PRU-34854

Problems Methods Pigeonhole principle Pigeonhole principle (other) Algebra and arithmetic Sequences Recurrent relations Recurrent relations (other)

12–14 3.0

In the number \(1234096\dots\) each digit, starting with the 5th digit is equal to the final digit of the sum of the previous 4 digits. Will the digits 8123 ever occur in that order in a row in this number?