Open nowWeek 12Number Theory
A Staircase of Sums
Let S = 1 + 2 + 3 + ⋯ + n. Find every positive integer n < 500 for which S is a perfect square, and prove that your list is complete.
Worth7 pts
AttemptsOne only
Closes
Need a nudge? Show hint
Write S in closed form. What does it mean for n(n+1)/2 to be a square, given that n and n+1 share no factors?
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