1- Find a pair (m,n) of positive integers such that K=∣2m−3n∣ in all of this cases :a)K=5
b)K=11
c)K=192-Is there a pair (m,n) of positive integers such that : ∣2m−3n∣=2017
3-Every prime number less than 41 can be represented in the form ∣2m−3n∣ by taking an Appropriate pair (m,n)
of positive integers. Prove that the number 41 cannot be represented in the form ∣2m−3n∣ where m and n are positive integers4-Note that 25+32=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 2m−3n , 3n−2m , 2m−3n where m and n are positive integers GMO-Gulf Mathmatical Olympiadnumber theory