jessica098
New member
- Joined
- Oct 20, 2008
- Messages
- 15
The problem I need help with is writing (and proving) a proposition about integers that are the sum of two squares.
I've found that if [a] is in integers modulo 8 (Z8), then the possible values for [a]^2 are 0, 1 and 4.
With that, I determined that if and [c] are in Z8, then the possible values of (^2+[c]^2) in Z8 are 0, 1, 2, 4, and 5 because:
0+0=0
0+1=1
0+4=4
1+0=1
1+1=2
1+4=5
4+0=4
4+1=5
4+4=8=0
What I'm asked to do now is complete the following proposition and prove it:
"For each integer a, if a is the sum of two squares, then ______."
I was given the following hint: The conclusion that you use should state something about what the integer a can be congruent to modulo 8.
Can anyone help me finish AND prove the proposition? I'm STUCK! Thank you in advance!!!!!!
I've found that if [a] is in integers modulo 8 (Z8), then the possible values for [a]^2 are 0, 1 and 4.
With that, I determined that if and [c] are in Z8, then the possible values of (^2+[c]^2) in Z8 are 0, 1, 2, 4, and 5 because:
0+0=0
0+1=1
0+4=4
1+0=1
1+1=2
1+4=5
4+0=4
4+1=5
4+4=8=0
What I'm asked to do now is complete the following proposition and prove it:
"For each integer a, if a is the sum of two squares, then ______."
I was given the following hint: The conclusion that you use should state something about what the integer a can be congruent to modulo 8.
Can anyone help me finish AND prove the proposition? I'm STUCK! Thank you in advance!!!!!!