cai bai ma tong hai so chinh phuong le khong la so chinh phuong do ai dua len zay?
de bai do co the phat bieu lai nhu sau:
"cho S la tap hop gom 3 so tu nhien co tinh chat sau:tong hai phan tu tuy y cua S la mot so chinh phuong ( vi du
S=[5,20,44] hoac S=[10,54,90] la ca tap hop thoa man dieu kien tren ). CMR trong tap hop S khong co qua mot so le.
De tuyen sinh 10 lop chuyen toan troung PHO THONG NANG KHIEU DHQGTPHCM 2007-2008"
loi giai
bai toan phu: chung minh rang so chinh phuong le chia cho 4 du 1.
that vay: voi moi n thuoc Z.
ta co (2n+1)^2= 4n^2+4n+1 chia cho 4 du 1
do vay ta co dieu phai chung minh.
gia su ba phan tu cua S la ba so le.
2a+1;2b+1;2c+1 (a,b,c thuoc N)
ta co 2a+1+2b+1=2(a+b+1) la so chinh phuong (gt)
ma 2(a+b+1)\2 suy ra 2(a+b+1)\4
suy ra a+b+1\2
tuong tu ta co b+c+1\2,c+a+1\2
do do ta co a+b+1+c+1+c+a+1 \ 2
suy ra 2(a+b+c+1)\2 vo li
vay ba phan tu cua S khong cung la so le
gia su ba phan tu cua S la hai so le va mot so chan
2x+1;2y+1;2z (x,y,z thuoc N)
ta co 2x+1+2y+1=2(x+y+1) la so chinh phuong (gt)
ma 2(x+y+1)\2 suy ra 2(x+y+1)\4
suy ra x+y+1 \2
ta cung co 2x+1+2z=2(x+z)+1 la so chinh phuong le
theo bai toan phu tren ta co 2(x+z)\4 suy ra x+z \ 2
lap luan tuong tu ta co y+z \ 2
do do x+y+z+1+x+z+y+z \ 2
suy ra 2(x+y+z)+1 \ 2 vo li
vay ba phan tu cua S khong the la hai so le va mot so chan
tom lai tap S co khong qua mot so le.
tuy day la mot de bai khac nhung van khong mat tinh tong quat.
Trang Chính 
mà chả rõ lý do 