+1 vote
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a mod n : tell the formula ?

+1 vote

In arithmetic modulo b, we express any $a$  as $nb + r$, where $r$ must be a non-negative integer.

-4 can be expressed as $-2 * 2 + 0$, So -4 mod 2 = 0

One good example would be -2 mod 6.

-2 can be expressed as $(-1 * 6) + 4$, so -2 mod 6 = 4.

Hope it's clear now.

selected
+1 vote
I dont give exact answer,but i can give you approach that i follows.

Lets say we have a number n (say 13),now if i find mod of this with some number(+ve) say m=4, it will give me 1(13%4).

Now suppose i add multiple of 4(4x) into n.Say 13+(4*2),will it change my Mode?No way ,right?

Now say i have -ve number -13,now if i add multiple of 4,that is greater that 13 say 16,now it becomes -13+16,which is 3%4=3.

Hope this clears,-4mod2,will be (-4+2*3)=(-4+6)=(2)mod2,which is 0.
ya right but tell

-9 mod 4 =3

rt?
there is a formula behind that

i searched google but it showing confusion. somebody know that

a mod n formula ?
@wanted: you're right.  -9 mod 4 indeed equals 3.

You can check my answer to get precise mathematical definition.
yes.You can write as (-9mod4)=(-9+12)mod4=(3)mod4=3
tie buddy