Ta có:a+b+c chia hết cho 2
=>(a+b+c)2 chia hết cho 2
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc=a2+b2+c2+2(ab+ac+bc)
mà 2(ab+ac+bc) chia hết cho 2
=>a2+b2+c2 chia hết cho 2
=>P là hợp số
cho x,y,z la cac so nguyen duong va x+y+z la so le, cac so thuc a,b,c thoa man (a-b)/x=(b-c)/y=(a-c)/z. chung minh rang a=b=c
Tim a,b la cac so nguyen duong sao cho a+b^2 chia het cho a^2b-1
B1. Cho f(1)=1008,f(1)+f(2)+...+f(n)=n^2.f(n) f(n)la ham so duong
tinh f(2015)
B2 Cho cac so nguyen to q,p,r,s sao cho cac so sau deu la so nguyen to p^s+s^q,q^s+s^r,r^s+s^p
tim cac so p,q,r,s
B3 co a,b,c duong a mu 3+bmu3=c^3
so sanh a^2015+b^2015 va c^2015
Cho a, b, c, d la cac so nguyen duong thoa man a2+b2=b2+d2. CM a+b+c+d la hop so
cho a,b,c,x,y,z la cac so nguyen duong thoa man a^x=bc;b^y=ac;c^z=ab. chung minh xyz-x-y-z=2
voi a,b la cac so nguyen duong sao cho a+1 va b+2007 chia het cho 6
cmr 4a+a+b chia het cho 6
bai 1 tim cac stn x y z sao cho x+y+z=xyz
bai 2cmr neu m^2+mn+n^2chia het cho 9 voi m ,n la cac stn thi m,n chia het cho 3
bai 3 tim stn n nho nhat de cac phan so sau toi gian
7/n+9.8/n+10,...,31/n+33
bai 4chung to rang phan so m^3+2m/m^4+3m^2 +1 toi gian
bai 5 a,cmr khong ton tai so chinh phuong nao co dang abab
b,cho 51 so nguyen duong khong vuot qua 100 cmr ton tai 2 so trong 51 so noi tren ma 1 so chia het cho so con lai
c,tim cac so co 3 chu so sao cho hieu cua so ay va gom 3 chu so ay viet theo thu tu nguoc lai la mot so chinh phuong
bai 6cmr A=2x(x+y-1)+y^2+1 luon nhan gia tri khong am voi moi x,y
bai 7 tim hai so nguyen duong sao cho tong ,hieu thuong (so lon chia cho so nho )cua chung cong lai duoc 38
bai 8 cho ba so a,b,c thoa man a/2009=b/2010=c/2011
tinh gia tri cua bieu thuc M=4(a-b)(b-c)-(c-a)^2
a) duong thang c co vuong goc voi duong thang b ko vi sao
b)cho doan thang d cat 2 duong thang a va b tai A va B cho niet goc A1= 115do . Tinh so do cac goc B2,B3,A3
c)goi AX va By lan luot la tia phan giac cua cac goc A1 va B CHUNG MINH Ax song song By
B1: cho a,b,c la cac so nguyen duong
CMR:neu a /b >hoac bang c/d thi a/b > hoac bang a+c/b+d > hoac bang c/d
B2: Tim PS nho nhat khac 0 sao cho khi chia no cho 14/9 ; cho 45/27 deu duoc thuong la cac so tu nhien
B3:CMR: 1/2^2 + 1/4^2 + 1/6^2 +....+ 1/100^2 < 1/2