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IF m^2+1 is even then 2n+m is odd. use direct proof

Sagot :

Pathogenicidn
First, it's important to know that 1. Odd + odd = even ex. 1+1=2 2. 2 times any counting number is equal to even ex. 1 x 2 = 2 3. Even + odd = odd ex. 2+1=3 Then we can say that m^2 is odd because if it is added to 1, the result is even (as shown in number 1) And because m^2 is odd, then m is odd because it sqaure root will not result to even when the square is odd. Therefore we can say that 2n+m is odd because 2n is even (example #2) and adding odd to that will result in an odd number (#3 example).
Jeremiaidn
2n + m is odd because in m^2 + 1, it is said to be even so if you remove the one, the resulting term which is m^2 will be odd so as its square root m. That means, m is odd and if it is added to 2n which is even because any number multiplied by 2 willl be eventhen 2n + m is odd becausea number + odd yields odd.