i was tring to solve this problem So i`ve to calculate the minimum value of
N so that phi(n)=k
here what i was thinking in :
we could rewrite "k" such that
k=((a-1)*a^x)*((b-1)*b^y) ...... and so on where a,b are primes and x,y some values i`ve to find
then i`ve calculated all the primes where k%(p-1)==0 sorted in increasing order
then for each prime (p) brute force to get the power "a" such that "a" is the maximum value satisfy this relation
k%((p-1)*p^a)==0
then get the new k
k=k/((p-1)*p^a)
then Do the same using the next prime till the k reach 1
after reconstruct N using the primes and it`s values
but this solution dose not work . May some one help in how i could calculate the inverse eular ?!