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.
If there are three roads from Goshen to Gravette and two roads from Gravette to Tontitown, how many ways are there to go from Goshen to Tontitown through Gravette?
Design a single error correcting code for m=3 & n=7
Set up a number pattern with six terms for square numbers
4C2 is equal to _____________
Proof of rational points on the general form of conic sections?
A. Determine if 1781 is divisible by 3, 6, 7, 8, and 9. (5 items x 2 points)
B. Determine if each of the following numbers is a prime or composite.
6. 828
7. 1666
8. 1781
9. 1125
10. 107
C. Find the greatest common divisor of each of the following pairs of integers.
11. 60 and 100
12. 45 and 33
13. 34 and 58
14. 77 and 128
15. 98 and 273
D. Find the least common multiple of each of the following pairs of integers.
16. 72 and 108
17. 175 and 245
18. 150 and 70
19. 32 and 27
20. 540 and 504