using-PMI-show-that-n-2-the-number-5-n-ends-with-the-digits-25-

Question Number 33462 by NECx last updated on 17/Apr/18

u s i n g P M I s h o w t h a t \forall n ⩾ 2 t h e

n u m b e r 5^{n} e n d s w i t h t h e d i g i t s 25

Answered by MJS last updated on 17/Apr/18

b a s e :

n = 2

5^{2} = 25

if true for n \Rightarrow true for n + 1

i, j \in N

5^{n} = 100 i + 25 \Rightarrow 5^{n + 1} = 100 j + 25

5^{n + 1} = (100 i + 25) \times 5 = 500 i + 125 =

= 500 i + 100 + 25 = 100 j + 25 with

j = 5 i + 1

this holds for n ⩾ 2

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