Prove that the following numbers are composite: 1000!+2 and 1000!+3
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Prove that the following numbers are composite: 1000!+2 and 1000!+3
2 divides 1000! + 2Quote:
Originally Posted by algebrapro18
and 3 divides 1000! + 3
do you recall what 1000! means?
1000! + 2 is even. Therefore ........Quote:
Originally Posted by algebrapro18
1000! + 3 = 3 [(1)(2)(4)(5) ....... (1000) + 1] and so clearly has positive divisor other than one or itself ......
Using this idea we can prove that we consecutive composite numbers has no bound to it. Becauseare all composite thus we can make the list of composites as long as we wish.
This is the basis for a classic Challenger:
Find 99 consecutive composite numbers.
Answer (drag your cursor between the asterisks)
* 100! + n, for n = 2,3,4,5, ... , 100 *