MathDB
Show that this ceil is even

Source: Brazil EGMO TST1 2023 #2

January 29, 2024
algebranumber theoryceiling functionprime numbers

Problem Statement

Let pp and qq be distinct odd primes. Show that ⌈pq+qp−pq+1pq⌉\bigg\lceil \dfrac{p^q+q^p-pq+1}{pq} \bigg\rceil is even.
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