⚠ WARNING :REALLY HARD PROBLEM ⚠

Question

Write a program to find all positive integers n, k1, k2,..., kn such that: k1+k2+... +kn = 5n-4 and 1/k1+1/k2+...+1/kn = 1

Hint: n<10

Answer 1

1 is the only number that works
since 1/1 = 1 add anything else to 1 and you are > 1 you will never have anything else work for 1/k1 + ... = 1
1/k1 ... 1/kn additive will approach 2 but never get there......

Assuming I am reading the problem right.