perplexus.info :: Just Math : Lasts a year

Lasts a year (Posted on 2011-10-24)

Every 8-digit number structured ABCXABCX, where A,B and C are not necessarily distinct, is divisible by 365 iff X equals either 5 or 0.

Why?

No Solution Yet Submitted by Ady TZIDON

Rating: 3.6667 (3 votes)

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Put another way

Comment 5 of 5 |

ABCXABCX = 10001 * ABCX

10001= 73 * 137

ABCX has factor 5 if and only if X is 5 or 0.

When ABCX is divisible by 5, that's when 10001 * ABCX is divisible by 73 * 5 = 365.

Posted by Charlie on 2011-10-25 09:09:40

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