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Divisibility rule (Posted on 2013-02-13) Difficulty: 2 of 5
abcde is five digit number. Show that abcde is divisible by 7 if and only if the number abcd-(2*e) is divisible by 7 (* means Multiplication)

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution full proof - spoiler Comment 1 of 1

Denote concatenation  xyzw by bold letters ,-and multiplication    xyzw by regular font.

n1 = abcde= 10*abcd +e

 n2 =10* (abcd -2e)=10*abcd -20e

n1-n2= 21*e    is divisible by 7.


Reading the 3 lines to fro makes it if and only if.

  Posted by Ady TZIDON on 2013-02-13 11:05:20
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