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nice-calculus-suppose-that-m-4-p-1-3-where-p-is-a-prime-number-and-p-gt-3-prove-that-2-m-1-m-1-




Question Number 128246 by mnjuly1970 last updated on 05/Jan/21
              ...nice  calculus...    suppose that  :: m=((4^p −1)/3) ,  where         p  is  a prime number and  p>3.  prove  that  :::                  2^(m−1)  ≡^m  1    ...?
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{suppose}\:{that}\:\:::\:{m}=\frac{\mathrm{4}^{{p}} −\mathrm{1}}{\mathrm{3}}\:,\:\:{where} \\ $$$$\:\:\:\:\:\:\:{p}\:\:{is}\:\:{a}\:{prime}\:{number}\:{and}\:\:{p}>\mathrm{3}. \\ $$$${prove}\:\:{that}\:\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{{m}−\mathrm{1}} \:\overset{{m}} {\equiv}\:\mathrm{1}\:\:\:\:…? \\ $$$$\: \\ $$

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