Divisibility Test Note 3

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.

#NumberTheory #Divisibility #Sharky

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

DIVIDE 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

DHIRAJ KUMAR - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$