# -*- coding: utf-8 -*-
"""
Created on Tue Jun 13 14:31:25 2023
RMS 2023 - 986
"""

from math import gcd as pgcd

def determiner(n):
    """
    Renvoie l'expression irréductible du n-ième nombre harmonique
    """
    p, q = 0, 1
    for k in range(1, n+1):
        num = k*p + q
        den = k*q
        d = pgcd(num, den)
        p, q = num//d, den//d
    return p, q

premiers = [True]*101
premiers[0] = False
premiers[1] = False

for n in range(2, 101):
    if premiers[n]  :
        i = 2*n
        while i<101:
            premiers[i] = False
            i += n

P = []
for i, x in enumerate(premiers):
    if x:
        P.append(i)

for n in P:
    p, q = determiner(n-1)
    r = p%(n**2)
    print("n = {} - reste = {}".format(n, r))