Combinatorics | Number Theory Answers

Find solution of:

a)"4x" is identical to 3 mod 7

b)"9x" is identical to 11 mod 26

c)"8x" is identical to 6 mod 14

d) "8x" is identical to 6 mod 422

What is the largest integer n which makes n3 + 100 is divisible by n + 10

Determine the first 4 terms in the bionomial expansion (1+2x)^-3/4

, Let k be an arbitrary natural number and p a prime number if k² is a multiple of p then necessarily;

A.     K is an odd number

B.     K is a prime number

C.     K is a multiple of P

D.     None of the above

The remainder of n7 is 4. The remainder of m9 is 7. Which of the following is a potential value for n×m?

(A) 24

(B) 44

(C)22

(D) 126

(E) 55

1.   Subtract the binary numbers 1110₂ from 10101₂

Demonstrate how you add the numbers 111_2, 110_2, 1100_2, 101_2, and 1111_2.  Check your answer by calculating the decimal numbers for the above.

Show that if n ∣ m, where n and m are integers greater than 1, and if a ≡ b (mod m), where a and b are integers, then a ≡ b (mod n).

Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.