Find and prove the divisibility test for 13. Furthermore, prove the test for \(13^n\).

As you can see, the tests are becoming harder as we progress up the prime ladder.

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## Comments

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TopNewestDIVIDE THE NO . IN GRS. OF 3 DIGITS FROM RIGHT SIDE NO THEM AS 1ST GR.,2ND GR. ,3RD GR. ETC TILL END.NOW ADD ALL EVEN GR S.& ADD ALL ODD GRS. NOW TAKE DIFFERENCE OF SUM OF EVEN GRS & SUM OF ODD GRS. NOW IFF THE DIFFERENCE IS DIVISIBLE BY EITHER OF 7 OR 11 OR 13 THEN THE ORIGINAL NO IS DIVISIBLE BY THAT NO 7 OR 11 OR13 EXAMPLE 323323 HERE 323-323=0 HENCE NO IS DIVISIBLE BY ALL 7,11,&13 38077== 77-38=39 SINCE 39 IS DIVISIBLE BY 13&NOT BY 11 OR 7 HENCE NO 38077 IS DIVISIBLE BY ONLY13 &NOT BY 7 OR 11

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