chung to rang so nguyen to p;p>5 khi chia cho 6 co the du 1 hoac 5

2)chung minh rang neu p va p+2 la so nguyen to lon hon 3 thi p+1 la mot hop so

Chung minh rang l x l lon hon hoac bang 0

cho 70 so nguyen duong phan biet a1;a2;a3;.......;a70,moi so khong vuot qua 200. Chung minh rang ton tai2 trong 70 so da cho sao cho hieu chung bang 4 hoac bang 5 hoac bang 9

Hai so tu nhien a va b chia cho m co cung so du , a lon hon hoac bang b . chung to rang a- b:m

1.     cho 4 stn a lon hon hoac bang b, b lon hon hoac bang c, clon hon hoac bang d.

CM:(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)

2.      CM: co the tim dc 1 stn k sao cho: (1997^k)-1 chia het cho 10^4

3.      tong cac chu so cua 1 so chinh phuong co the bang 1995 dc k?

4.      tong cua 1995 stn khac 0 dung bang 1995. Hoi UCLN cua chung la bao nhieu?

cho A = 1+2+3+4+...+n va B = 2n + 1 ( voi n thuoc N , n lon hon hoac bang 2)   chung minh A va B la hai so nguyen to cung nhau

Tim x biet:

A. (x-3/4).(3x+1/2)lon hon hoac bang 0 

B. (2x+1).(4x+3)be hon hoac bang 0

cho p la so nguyen to lon hon 3 

a] chung to rang p 6k+1 hoac 6k+5 

b] biet 8p +1 la so nguyen to chung minh 4p+1 la hop so

cho6 so tu nhien khac nhau co tong la 50.chung minh rang trong 6 so tu nhien da cho ton tai 3 so co tong lon hon hoac bang 30