Assume you have a predicate Pn You know that P8 is true and

Assume you have a predicate P(n). You know that P(8) is true and

that P(k) P(k + 5). For what values of n do you know that P(n) is true? Write your answer using mod arithmetic

Solution

Since we know that P(8) is true, and

if P(8) is true then P(8+5) is also true.

so, P(n) is true for n=8,13,18,....i.e n= 5k+8 or

P(n) is true if n =8 (mod 5) = 3 (mod 8)