MathLabs

Problem 1

Let pp and qq be positive integers such that pq=1−12+13−14+⋯−11318+11319\dfrac pq=1-\dfrac12+\dfrac13-\dfrac14+\cdots-\dfrac1{1318}+\dfrac1{1319}. Prove that pp is divisible by 19791979.
Step 2 of 4: Pair terms from the two ends
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660+1319=1979660+1319=1979
Detailed analysis

There are 660 terms, so pair the first with the last, the second with the next-to-last, and so on. Every pair has denominator factors whose numerator sum is 1979.