perplexus.info :: Just Math : Maximum Power 2 Divide Evenly

Maximum Power 2 Divide Evenly (Posted on 2008-10-19)

Determine the maximum value of a positive integer G, such that (2007¹⁰²⁴ -1) is evenly divisible by 2^G.

Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (2 votes)

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Comment 2 of 2 |

(2007¹⁰²⁴-1) EQUALS

(2007⁵¹²+1)(2007²⁵⁶+1)(2007¹²⁸+1)(2007⁶⁴+1)(2007³²+1)(2007¹⁶+1)(2007⁸+1)(2007⁴+1)(2007²+1) (2007+1)) (2007-1)

first 9 factors are divisible each by 2

(2007+1) divusible by 8 and (2007-1) by 2

So G=9+3+1=13

Posted by Ady TZIDON on 2008-10-19 17:31:16

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