Show that if n divides m where m and n are positive integers greater than 1, then a ≡ b (mod m) implies a ≡ b (mod n) for any positive integers a and b.

Assessed Exercise 2 2
1. (a) [4]Show that if n divides m where m and n are positive integers greater than 1, then a ≡ b (mod m) implies a ≡ b (mod n) for any positive integers a and b.

(b) [3]Show that a·c ≡ b·c (mod m) with a, b, c and m integers with m≥2 does not
imply a ≡ b (mod m).

2. [5]A company has a contract to cover the four walls, ceiling, and floor of a factory building with fire-retardant material. The building is rectangular where of width 280m, length 336m and height 168m. Square panels can be manufactured in any size of whole metres.
For safety reasons, the building must be covered in complete panels (i.e. panels cannot be cut). What is the minimum number of equally sized square panels that are required to line the interior of the building? Explain your answer.

3. [5]Prove that least significant digit of the square of an even integer is either 0, 4, or 6.

Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respectively.
4. [5]Use mathematical induction to show that for any n ∈ N, if n ≥ 2, then
nY
i=2

1 − 1
i2

= n+1
2·n .
5. [5]Use mathematical induction to show that 2 divides n2 − n for all n ∈ N.

Brilliant Essay Help

Show that if n divides m where m and n are positive integers greater than 1, then a ≡ b (mod m) implies a ≡ b (mod n) for any positive integers a and b.

Make your order right away

Confidentiality and privacy guaranteed

satisfaction guaranteed