1.

If a -= b (mod m), then which of the following is not always true ?

Answer»

`a^(2) -= b^(2)` (mod m)
`a+m -= b +m` (mod 2m)
`am -= bm` (mod `m^(2)`)
`a+m -= b - m` (mod 2m)

Solution :(i) Use the condition `a -= b` (mod m) `RARR a-b` is divisible by m.
(II) Verify WHETHER each options SATISFIES the above conditions or not.
(iii) Refer the properties of congruence modulo.


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