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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: Cho : M = 5⁶¹ + 25³¹ + 125²¹ Chứng minh rằng : M chia hết cho 31

Toán Lớp 6: Cho : M = 5⁶¹ + 25³¹ + 125²¹
Chứng minh rằng : M chia hết cho 31

Comments ( 2 )

  1. $\text{M = 5⁶¹ + 25³¹ + 125²¹}$
    $\text{=5⁶¹+(5²)³¹+(5³)²¹}$
    $\text{=5⁶¹+5²·³¹+5³·²¹}$
    $\text{=5⁶¹+5⁶²+5⁶³}$
    $\text{=5⁶¹(1+5+5²)}$
    $\text{=5⁶¹(1+5+25)}$
    $\text{=5⁶¹.31}$
    $\text{31 chia hết cho 31}$
    $\text{⇒ 5⁶¹.31 chia hết cho 31}$
    $\text{Hay M chia hết cho 31}$

  2. M= 5^61 + 25^31 + 125^21
    M= 5^61 + (5^2)^31 + (5^3)^21
    M= 5^61 + 5^62 + 5^63
    M= 5^61 ( 1 + 5 + 5^2)
    M= 5^61 . 31 vdots 31
    Vậy M vdots 31

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222-9+11+12:2*14+14 = ? ( )

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