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Sum the integers, get squares? (Posted on 2007-04-05) Difficulty: 2 of 5
Can the sum of any 2112 consecutive positive integers be a perfect square?

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (3 votes)

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Solution solution | Comment 3 of 5 |

x + (x+1) + ... + (x+2111) = (2x+2111) * 1056

(2x+2111) is odd (has no factor of 2)

2 appears as a factor in 1056 (and therefore the whole total), five times, which is odd, so the 2's can't be separated equally into two equal factors (that being what a square root is).


  Posted by Charlie on 2007-04-05 10:25:45
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