MathDB

1- Find a pair

(m,n)

of positive integers such that

K = |2^m-3^n|

in all of this cases :

a) K=5

b) K=11

c) K=19

2-Is there a pair

(m,n)

of positive integers such that :

|2^m-3^n| = 2017

3-Every prime number less than

41

can be represented in the form

|2^m-3^n|

by taking an Appropriate pair

(m,n)

of positive integers. Prove that the number

41

cannot be represented in the form

|2^m-3^n|

where

m

and

n

are positive integers
4-Note that

2^5+3^2=41

. The number

53

is the least prime number that cannot be represented as a sum or an difference of a power of

2

and a power of

3

. Prove that the number

53

cannot be represented in any of the forms

2^m-3^n

3^n-2^m

2^m-3^n

where

m

and

n

are positive integers

Problem Statement