Question

Show that any number of the form 4n nen can never end with the digit 0

Answer 1

CONSIDERING THE MATHEMATICAL PROFILE OF SWITCHING OF NUMBERS OR SWITCH SYSTEM THEOREM ...

FOR THE APPLICATION OF 4 RAISED TO THE POWER "n" ...

IT HAS PERIOD OF 2 AND SWITCH NUMBER IS 1 , 0 ...

WHICH SPECIFIES THE VALUES OF THE GIVEN FORMAT WILL GET REPEATED AFTER EVERY SECOND VALUE OF "n"

AND IT'S PERIODICALLY VALUES OBTAINED IS 4 AND THEN 6 ...

HENCE , HERE CONCLUDE THAT THE GIVEN EXPRESSION CAN NEVER END WITH "0"

Answer 2

Step-by-step explanation:

→ No, 4ⁿ can never end with the digit 0 for any natural number n .

→ If 4ⁿ ends with 0 then it must have 5 as a factor .

But, 4ⁿ = ( 2² )ⁿ = 2²ⁿ .

→ It shows that 2 is the only prime factor of 4ⁿ .

Also, we know from the fundamental theorem of airthematic that the prime factorisation of each number is unique .

So, 5 is not a factor of 4ⁿ .

Hence, 4ⁿ can never end with the digit 0 .