cau 1 ,cho m,n thuoc n va p la so nguyen to thoa man p/m-1=m+n/p

CMRp^2=n+2

cau 2,cho a,b,c thoa man a+b+c=0 CMRab+bc+ca be hon hoac bang 0

cau 3,bay gio la 4 gio 10 phut hoi sau it nhat bao lau thi hai kim dong ho nam doi dien nhau tren mot duong thang

cau 4,so 2^100 viet trong he thap phan tao thanh 1 so hoi so do co bao nhieu chu so

cau 5,cho a,b,c la so do 3 canh cua mot tam giac vuong voi c la so do canh huyen CMRa^2n+b^2n be hon hoac bang c^2n (n la so tu nhien lon hon 0 )

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