For all m, n integers show that (m^2-n^2) mod (m-n) ≡m+n b. Prove or disprove: ∛n is irrational where n is the number as found in Q.1 if n is a prime number then use “n” else choose the immediate next prime to that integer.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.