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# how do i do algebraic proof? watch

1. so im a bit stuck on this type of question:

prove that 5^20 - 5^19 is even
the cgp book doesnt explain it at all and its not on hegartymaths, how do i do this style of question?
2. (Original post by Gent2324)
so im a bit stuck on this type of question:

prove that 5^20 - 5^19 is even
the cgp book doesnt explain it at all and its not on hegartymaths, how do i do this style of question?
odd*odd
odd-odd
3. (Original post by Gent2324)
so im a bit stuck on this type of question:

prove that 5^20 - 5^19 is even
the cgp book doesnt explain it at all and its not on hegartymaths, how do i do this style of question?
Just say then factorise
4. (Original post by Aph)
odd*odd
odd-odd
what do u mean

(Original post by RDKGames)
Just say then factorise
ok so i got 5(1x5^18 x5^18) how do i prove that that is even since 5x3 for instance isnt even
5. (Original post by Gent2324)
ok so i got 5(1x5^18 x5^18) how do i prove that that is even since 5x3 for instance isnt even
Not what I meant.

6. (Original post by Gent2324)
ok so i got 5(1x5^18 x5^18) how do i prove that that is even since 5x3 for instance isnt even
You can argue that the 2 numbers are odd very simply.
7. (Original post by Aph)
You can argue that the 2 numbers are odd very simply.
how?

(Original post by RDKGames)
Not what I meant.

wait im completely lost as to why its 5-1 and what do the dots mean?
8. prove that 5^20 - 5^19 is even:

5^20 - 5^19 = 5^19 (5-1) = 4 (5^19) = 2n where n=2.5^19

Or you can say that both end in 5 hence odd and odd-odd=even.
9. 5^20 - 5^19 = 5*5^19 - 5^19 = 5^19 *(5-1) = 4* 5^19 = 2*2*5^19 so it is even!
10. (Original post by Gent2324)
wait im completely lost as to why its 5-1 and what do the dots mean?
The dot means multiplication.

You're simply factoring out , so
11. (Original post by Gent2324)
how?

wait im completely lost as to why its 5-1 and what do the dots mean?
5^20 - 5^19.

Common factor is 5^19 so factor this:

5^19 [5^1 - 1] = 5^19 [4] = 2 [2 x 5^19] hence even.

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Updated: February 25, 2018
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