chung minh rang voi moi so tu nhien n, cac so sau la hai so nguyen to cung nhau:
a) 7n + 10 va 5n + 7
b) 2n +3 va 4n +8
chung to rang voi moi so tu nhien n th (2n+1)va2n^2-1la hai so nguyen to cung nhau
chung to rang voi moi so tu nhien N gia tri cua 2 bieu thuc 7n+10 va 5n+7 luon la 2 so nguyen to cung nhau
voi n so tu nhien thoa man 6n+1 va 7n-1 la hai so tu nhien khong nguyen to cung nhau thi uoc chung lon nhat cua 6n+1 va 7n-1 la bao nhieu
Chung minh rang voi moi so n thi 2 so sau nguyen to cung nhau
2n+5 va 2n+7
2n+5 va 3n+8
5n+7 va 2n+3
chung minh rang voi moi so tu nhien n # 0 thi:
a moi so nguyen to lon hon 2 deu co dang 4n _+1
b moi so nguyen t lon hon 3 deu co dang 6n +_1
chung to rang hai so 3n+4 va n+1 la hai so nguyen to cung nhau voi n la so tu nhien khac 0
cho n la so tu nhien bat ki ;chung minh rang (n+3) va(2n+5) la 2 so nguyen to cung nhau
Chung to rang:14n+3 va 21n+4 la so nguyen to cung nhau voi n la so tu nhien