find all positive integers n for which n! + 5 is a perfect cube.
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3 Answers
ninepointcircle
·2011-06-14 23:12:52
well its easy
See for n ≥ 10
last two digits will be 00 but
as any cube of form (5k) ends in 125
so n!+5 will end in 05 for n≥10
Jut check for n<10
answer is n=5 :)
Shubhodip
·2011-06-15 04:47:21
Alternative: (A.Titu)
for , n\geq 7 , n! + 5 \equiv 5 (mod 7) a contradiction for all cubes. we check for only n< 7 [6]