(a) Any integer with factorisation 5a .7b. 11° where a, b, c E N, is said to be 12-regular if and only if it satisfies t

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A Any Integer With Factorisation 5a 7b 11 Where A B C E N Is Said To Be 12 Regular If And Only If It Satisfies T 1 (92.82 KiB) Viewed 25 times

(a) Any integer with factorisation 5a .7b. 11° where a, b, c E N, is said to be 12-regular if and only if it satisfies the condition a+b+c= 12. How many 12-regular numbers are there? (b) Suppose x, y E Z. We shall write x ~ y, or say that 2 is equivalent to y, if and only if x = y(1,925)” for some n E Z. Let S be the set of 12-regular integers such that no two elements of this set are equivalent to each other. Then S can be written as s={50.76.114|a+b+c= 12 where a, b, c e N and A} = where A is the condition O a < 2 and b < 1 and c < 1. o a< 2 or b< 1 or c< 1. O a < 2 and b<1 and c < 1. a < 2 or b < 1 or c<1. (c) Hence, or otherwise, find |S||