Odd left behind

odd no.=even no+1.............

even no./2=0 (remainder)..................

but.................

even no+1(odd no)/2=1 (remainder)......................

If you take any odd number divided by 2 finally we will get remainder is 1.

This is so simple, if I will divide to 3 by 2, In this problems remainder will come 1, and 3 is an odd number, now divide to 5 by 2, in this case remainder will come same 1, so that is always remainder w ill come 1, if we will divided by 2 of any odd number.

Before every odd number there is an even no. When a odd no. is divided by 2, we get the quotient as the even no. before the given odd no. and the remainder as 1.

Odd number can be written as 2*m + 1 (where m is any integer). Keep subtracting 2 from it m times and we'd left out with a 1.

Since any number times 2 is even, being the definition of an even number, 2n+1/2=2(n+.5)/2=n+.5 because you add the +.5 multiply it by the divisor and you get 1, the remainder of any odd number

Todo número impar pode ser escrito da forma 2k+1, sendo k um número pertencente ao conjuntos dos números inteiros.

Sabendo que se a≡m(mod k) e b≡n(mod k). Temos: (a+b)≡(m+n)(mod k).

É fácil ver que:

2k≡0(mod 2) e 1≡1(mod 2).

Portanto 2k+1≡1(mod 2)

every odd number divides by 2 shows result will be one ..