Guest Posted March 15, 2010 Report Share Posted March 15, 2010 (edited) For any positive integer n, in the prime factorization of n! the largest prime number will always be greater than or equal to the largest exponent. Prove/Disprove the statement. Edited March 15, 2010 by K4D Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted March 15, 2010 Report Share Posted March 15, 2010 The proposition is incorrect. Look at 10! =2^8 * 3^4 * 5^2 * 7. The largest exponent is 8 but the largest prime is only 7. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 15, 2010 Report Share Posted March 15, 2010 well darn, I thought it would be an interesting puzzle, I think I skipped over 6 when I checked 10! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 15, 2010 Report Share Posted March 15, 2010 Not True! Quote Link to comment Share on other sites More sharing options...
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For any positive integer n, in the prime factorization of n! the largest prime number will always be greater than or equal to the largest exponent.
Prove/Disprove the statement.
Edited by K4DLink to comment
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