Question

已知2的m次方加3的n次方加5的p次方等于7,2的(m-1)次方加上3的n次方加5的（p+1）方等于11,求2的(m+1

Answer 1

2^(m-1)+3^n+5^(p+1)=11

2^m/2+3^n+5*5^p=11 (1)

2^m+3^n+5^p=7 (2)

(1)-(2)

-2^m/2+4*5^p=4

2^m=8(5^p-1)>0 5^p>1

2^m=8(5^p-1)代入(2)

3^n+9*5^p-8=7

3^n=15-9*5^p>0

5^p