Question

Prove step by step that 5^20-5^19 is an even number with out using a calculator Please can you tell me the steps and why?

Answer 1

9514 1404 393

Answer:

factor out 5^19

Explanation:

a) Reason from parity:

both 5^20 and 5^19 are products with only odd numbers (5) as factors. Hence each is an odd number. The difference of odd numbers is always even.

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b) Factor:

5^20 -5^19 = 5^19(5 -1) = 5^19×4

This product has an even factor (4), so is even.