Can you add 3 odd numbers and get an even number?

Question

14864 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-17T18:48:54

The sum of any three odd numbers equals an odd number.

Proof

Lets consider three odd numbers

#a=2x+1#
#b=2y+1#
#c=2z+1#

where #a,b,c# are integers and #x,y,z# integers as well

then the sum equals to

#a+b+c=2*(x+y+z+1)+1#

The last tell us that their sum is an odd.

Answer 2 · 2015-09-17T21:42:51

Yes, it is possible, but not in ordinary integer arithmetic.

In modular arithmetic with an odd modulus, every number is both odd and even.

For example, in arithmetic modulo #7# we find:

#1 + 3 + 5 = 9 = 2 = 2 * 1#