CMR (3^n+3+3^n-1+2^n+2+2^n+1)chia het cho 6 voi moi n thuoc N*
CMR n^3 - 2n^2 + 7n - 7 chia het cho n^2 + 3 voi moi n thuoc Z
CMR:a^3-13a chia het cho 6 voi moi a thuoc Z va a>1
cmr
3x+1+3x+2+..+3x+100 chia het cho 120 voi n thuoc N
1. CMR:\(3^{x+1}+3^{x+2}+3^{x+3}+.....+3^{x+100}\)chia het cho 120 (voi x thuoc N)
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
Tim n thuoc N biet:
a. n+3 chia het cho n2+1
b.2n+3 chia het cho 7
Bai 1: chung minh rang: voi moi so nguyen duong n thi:
\(3^{n+2}-2^{n+2}+3^n-2^n\)chia het cho 10
Bai 2: Chung to rang:
A=75.(4\(^{2004}\)+4\(^{2003}\)+....+4\(^2\)+4+1)+25 la so chia het cho 100
Bai 3: Chung minh rang 3a + 2b :17 [=] 10a +b :17 (a,b thuoc Z)
b, Cho da thuc f(x) =ax\(^2\)+ bx+c 9a,b,c nguyen)
CMR nếu f(x) chia hết cho 3 với mọi giá trị của x thì a,b,c đều chia hết cho 3 ?
Mau giup minh voi
chung to rang A=2^2n -1 chia het cho 5 voi n thuoc N ,n >2