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Show that the0:15:41

Show that the product of gcd(a, b) and lcm(a, b) is |ab|. [NT-Ch.2-S2.6] - Part 4

Prove that quotients0:10:35

Prove that quotients of the greatest common divisor have the gcd of 1

Show that for0:07:12

Show that for any integer c, if a|c and b|c, then lcm(a, b)|c [NT-Ch.2-S2.6] - Part 3

Show that gcd(a0:08:42

Show that gcd(a ,b) divides lcm (a, b) and gcd(a, b) = lcm(a, b) iff a = b [NT-Ch.2-S2.6] - Part 2

Definition of Least0:13:51

Definition of Least Common Multiple [NT-Ch.2-S2.6] - Part 1

Prove that 1+2^1+2^2+2^3+...+2^n=2^(n+1)-10:10:13

Prove that 1+2^1+2^2+2^3+...+2^n=2^(n+1)-1 for every positive integer n

Prove that 1*2^1+2*2^2+3*2^3+...+n*2^n0:09:39

Prove that 1*2^1+2*2^2+3*2^3+...+n*2^n = (n-1)*2^(n+1)+2 for every positive integer n

Prove that 1-2^2+3^3-4^2+...+(-1)^(n-1)n^2=(-1)^(n-1)(n(n+1))/20:15:09

Prove that 1-2^2+3^3-4^2+...+(-1)^(n-1)n^2=(-1)^(n-1)(n(n+1))/2 for every positive integer n

Show that gcd(a^(2^m)+1,0:20:19

Show that gcd(a^(2^m)+1, a^(2^n)+1)= 1 or 2 [NT-Ch.2-S2.5] - Part 15

Prove that a^(2^n)-1=(a-1)(a+1)(a^2+1)(a^4+1)+...+(a^2^(n-1)+1)0:10:59

Prove that a^(2^n)-1=(a-1)(a+1)(a^2+1)(a^4+1)+...+(a^2^(n-1)+1) for every positive integer n

Prove that a^(n+1)-1=(a-1)(a^n+a^(n-1)+...+a+1)0:09:36

Prove that a^(n+1)-1=(a-1)(a^n+a^(n-1)+...+a+1) for every positive integer n

Show that gcd(n^3+2n,0:06:14

Show that gcd(n^3+2n, n^4+3n^2+1)=1 for every positive integer n [NT-Ch.2-S2.5] - Part 14

There are infinitely0:07:20

There are infinitely many integers x and y satisfying x+y=100 and (x, y)=5 [NT-Ch.2-S2.5] - Part 13

Show that there0:04:23

Show that there are no integers x and y satisfying x+y=100 and (x, y)=3 [NT-Ch.2-S2.5] - Part 12

Show that f(x)=1/sqrt(x^2-4)0:18:19

Show that f(x)=1/sqrt(x^2-4) is continuous on (-\infty,-2) and (2, 3]

Show that ((a^)2^n+1)|((a^)2^m-1)0:07:38

Show that ((a^)2^n+1)|((a^)2^m-1) [NT-Ch.2-S2.5] - Part 11

Show that if0:17:10

Show that if gcd(a, b)=c, then gcd(a^2, b^2)=c^2 [NT-Ch.2-S2.5] - Part 10

Show that f(x)=sqrt(9-x^2)0:14:46

Show that f(x)=sqrt(9-x^2) is continuous on the close interval [-3, 3]

Show that if0:05:56

Show that if gcd(a,b)=1 and gcd(a,c)=1, then gcd(a, bc)=1 [NT-Ch.2-S2.5] - Part 9

Find integers x0:05:22

Find integers x and y satisfying 93x-81y = 3 [NT-Ch.2-S2.5] - Part 8

Find integers x0:03:55

Find integers x and y satisfying 43x+64y = 1 [NT-Ch.2-S2.5] - Part 7

Find integers x0:08:19

Find integers x and y satisfying 71x-50y = 1 [NT-Ch.2-S2.5] - Part 6

Find integers x0:07:01

Find integers x and y satisfying 243x+198y = 9 [NT-Ch.2-S2.5] - Part 5

Find gcd(5767, 4453)0:10:36

Find gcd(5767, 4453) by using the Euclidean Algorithm [NT-Ch.2-S2.5] - Part 4