Problem #PRU-73620

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–15 3.0

Problem

Author: L.N. Vaserstein

For any natural numbers $a_{1}, a_{2}, \dots, a_{m}$ , no two of which are equal to each other and none of which is divisible by the square of a natural number greater than one, and also for any integers and non-zero integers $b_{1}, b_{2}, \dots, b_{m}$ the sum is not zero. Prove this.

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