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
cho hai số tự nhiên m và n thỏa mãn m+1/n+n+1/m la so nguyen chung minh rang uoc chung lom nhat cua m va n khong lon hon can bac hai cua m+n
chung minh rang: N=444...44 888...8 9(nchu so 4)( n-1 chu so 8) la so chinh phuong
chung minh rang trong hai so duong
a, so nao lon hon thi co binh phuong lon hon
b, so nao co binh phuong lon hon thi so do lon hon
biet a+1 va 2a+1 (a thuoc N) dong thoi la 2 so chinh phuong. chung minh rang a chia het cho 24
1 stn so 1c/s1 2c/s2 3c/s3 4c/s4 co the la so chinh phuong khong vi sao
Cho n thuoc N va n-1 khong chia het cho 4
CMR : 7^n +2 khong la so chinh phuong
cho p la so nguyen to lon hon 3 chung minh rang p^2-1 chia het cho 24
Cho: A,B trong do Agom 2m chu so 1 , B gom m chu so 4
Chung minh rang A+B+C+1 la so chinh phuong