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Divisibility Sequence (Posted on 2025-01-30)

Show that every number in the sequence

1007, 10017, 100117, 1001117, 10011117, . . .

is divisible by 53.

No Solution Yet Submitted by Danish Ahmed Khan

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and another

| Comment 3 of 4 |

The first number, 1007, is 53*19.

Each successive number is obtained by multiplying the previous number by 10 then subtracting 53.

If x is 0 mod 53 then 10x-53 is also 0 mod 53

Posted by Larry on 2025-01-30 12:07:41

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