85 lines
5.6 KiB
HTML
85 lines
5.6 KiB
HTML
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<h2>(prime-k) factorial</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 381</h3><span style="width:300px;color:#666;">Published on Saturday, 21st April 2012, 05:00 pm; Solved by 1348</span></div>
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For a prime p let S(p) = (<img src='images/symbol_sum.gif' width='11' height='14' alt='∑' border='0' style='vertical-align:middle;' />(p-k)!) mod(p) for 1 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> k <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 5.
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For example, if p=7,<BR />
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(7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872.<BR />
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As 872 mod(7) = 4, S(7) = 4.
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It can be verified that <img src='images/symbol_sum.gif' width='11' height='14' alt='∑' border='0' style='vertical-align:middle;' />S(p) = 480 for 5 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> p <img src='images/symbol_lt.gif' width='10' height='10' alt='<' border='0' style='vertical-align:middle;' /> 100.
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Find <img src='images/symbol_sum.gif' width='11' height='14' alt='∑' border='0' style='vertical-align:middle;' />S(p) for 5 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> p <img src='images/symbol_lt.gif' width='10' height='10' alt='<' border='0' style='vertical-align:middle;' /> 10<sup>8</sup>.
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