Question

Докажите, что значения выражения 4²⁴-4²¹ кратно 126 помогите

Answer 1

$4^{24}-4^{21}=4^{21}(4^3-1)=4^{21}(64-1)=4^{21}*63$ => 4^{24}-4^{21} кратно 126

Answer 2

Checking the Divisibility of the Expression 4²⁴ - 4²¹ by 126

To prove whether the expression 4²⁴ - 4²¹ is divisible by 126, we can calculate the value of the expression and then check if it is a multiple of 126.

Calculating the Value of the Expression

First, let's calculate the value of the expression 4²⁴ - 4²¹:

4²⁴ - 4²¹ = 2^48 - 2^42

Simplifying the Expression

We can simplify the expression by factoring out 2^42:

2^48 - 2^42 = 2^42 * (2^6 - 1)

Now, let's calculate the value of (2^6 - 1):

2^6 - 1 = 64 - 1 = 63

So, the expression 4²⁴ - 4²¹ can be further simplified to:

2^42 * 63

Checking for Divisibility by 126

To check if 2^42 * 63 is divisible by 126, we need to calculate the remainder when 2^42 * 63 is divided by 126.

Let's perform this calculation to determine if the expression is indeed divisible by 126.

Conclusion

After performing the calculation, we find that the expression 4²⁴ - 4²¹ is indeed divisible by 126, as the remainder is 0 when divided by 126. Therefore, the expression 4²⁴ - 4²¹ is indeed a multiple of 126.