Question

Determine whether or not the function f:ZxZ->Z is onto if f(m,n)=m^2+n^2

Answer 1

the square of an integer is and integer,
the sum of integers is an integer ,

Answer 2

so

Answer 3

onto
for every pair in z

Answer 4

the answer at the end of book say not onto?

Answer 5

for every integer , its square is again an integer. Sum of such two integers is again an integer so the function is well defined
but the converse is not true
take 5 you can not find two intgers whose square is 5
so the function is not onto
please take 15 not 5
15 is not sum of two squares

Answer 6

thanks brother