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The digits of a five-digit number are MNOPQ. Prove that MNOPQ is divisible by 7 if and only of the number MNOP - 2 x Q is divisible by 7.
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Hello, mathisgood!
The digits of a five-digit number are
Prove that is divisible by 7 if and only of the number is divisible by 7.
[1] Given: . is divisible by 7.
. . .Prove: . is divisible by 7.
We have: .
Subtract
Divide by 10: .
Since is an integer, then is a multiple of 10: .
And we have: .
Therefore: . is divisible by 7.
[2] Given: . is divisible by 7.
. . .Prove: . is divisible by 7.
We have: .
. . . Then: .
Multiply by 10: .
. . Add
And we have: .
Therefore: . is divisible by 7.