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Find the smallest positive integer $N$ with the following property: of the three numbers $N$, $N+1$, and $N+2$, one of them is divisible by $2^2$, one of them is divisible by $3^2$, one is divisible by $5^2$, and one is divisible by $7^2$.

 Jul 25, 2020
 #1
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The smallest number that works is 1223 (1224 is divisible by 4 and 9, 1225 is divisible by 25 and 49).

 Jul 25, 2020
 #2
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The smallest positive n =98, 98+1, 98+2=98, 99,100

 

100 mod 2^2 =0

100 mod 5^2 =0

99 mod 3^2   =0

98 mod 7^2   =0

 Jul 25, 2020

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