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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 3^2, one of them is divisible by 5^2, one is divisible by 7^2, and one is divisible by 9^2, and one is divisible by 11^2.

 Feb 2, 2022
 #1
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7299 m0d 3^2 ==0

 

7300 m0d 5^2 ==0

 

7301 mod 7^2 ==0

 Feb 2, 2022
 #2
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N==3,351,698,  N+1==3,351,699,  N+2==3,351,700


3,351,698 mod 49==0
3,351,699 mod 9 ==0
3,351,700 mod 25==0
3,351,699 mod 81==0
3,351,700 mod 121==0

 Feb 2, 2022
 #3
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N==470,448,   N + 1==470,449,  N + 2==470,450

 

These also work!

Guest Feb 2, 2022

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