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    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?
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    (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
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    (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 5^{20} - 5^{19} = 5\cdot 5^{19} - 5^{19} then factorise
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    (Original post by Aph)
    odd*odd
    odd-odd
    what do u mean

    (Original post by RDKGames)
    Just say 5^{20} - 5^{19} = 5\cdot 5^{19} - 5^{19} 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
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    (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.

    5\cdot 5^{19} - 5^{19} = (5-1)\cdot 5^{19}
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    (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.
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    (Original post by Aph)
    You can argue that the 2 numbers are odd very simply.
    how?

    (Original post by RDKGames)
    Not what I meant.

    5\cdot 5^{19} - 5^{19} = (5-1)\cdot 5^{19}
    wait im completely lost as to why its 5-1 and what do the dots mean?
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    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.
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    5^20 - 5^19 = 5*5^19 - 5^19 = 5^19 *(5-1) = 4* 5^19 = 2*2*5^19 so it is even!
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    (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 5^{19}, so 5\times 5^{19} - 5^{19} = (5-1)\times 5^{19}
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    (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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