Question

prove that 2 raise to 10 + 5 raise to 12 is a composite number​

Answer 1

Answer:

how can i prove this fullish question

Step-by-step explanation:

ooo my god

Answer 2

Answer:

14657×16657.

Step-by-step explanation:

Use the binomial formulas. From

(2^5+5^6)2=2^10+2⋅2^5⋅5^6+5^12

we conclude

2^10+5^12=(2^5+5^6)^2−(10^3)^2=(2^5+5^6+10^3)(2^5+5^6−10^3)

2^10+5^12=(5^3)^4+4(2^2)^4=125^4+4⋅4^4

And then the result follows from Sophie Germain's identity, ie,

a^4+4b^4=(a^2+2ab+2b^2)(a^2−2ab+2b^2)

Yielding,

2^10+5^12=(5^6+10^3+2^5)(5^6−10^3+2^5)=16657⋅14657

Hint:

Use the Sophie Germain identity:

x^4+4y^4=(x^2+2xy+2y^2)(x^2−2xy+2y^2)=((x+y)^2+y^2)((x−y)^2+y^2)

5^12+2^10=(5^3)^4+4⋅(2^2)^4

2^10+5^12=(2^5)^2+(5^6)^2  =(2^5+5^6)^2−2⋅2^5⋅5^6 =(2^5+5^6)2−(2⋅5)^6 =(2^5+5^6)^2−(10^3)^2 =(2^5+5^6−10^3)(2^5+5^6+10^3) =(15657−1000)(15657+1000) =14657×16657.