Solutions for math problems with C++

URL to the problem page:  https://rosettacode.org/wiki/Hamming_numbers Hamming numbers are numbers of the form H = 2 i  × 3 j  × 5 k where i, j, k ≥ 0 Hamming numbers are also known as ugly numbers and also 5-smooth numbers (numbers whose prime divisors are less or equal to 5). Show the first twenty Hamming numbers. Show the 1691 st  Hamming number (the last one below 2 3 1 ). #include   <iostream> using   namespace   std ; long   long   int   power ( int   a ,  int   b ) {      long   long   int  result =  1 ;      for  ( int  i =  0 ; i < b; i++) {         result *= a;     }      return  result; } int   main () {      int  cnt, a =  0 , tmp;      long   long   int   numbers [ 20000 ] = {  0  }, smallest;     cout <<  "First 20 Hamming numbers are:"  << endl;      for  ( int  n =  0 ; a <  20000 ; n++) {          for  ( int  i =  0 ; i <= n; i++) {              for  ( int  j =  0 ; j <= n; j++) {                  for  ( i

URL to the problem page:  http://rosettacode.org/wiki/Happy_numbers A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers. Find and print the first 8 happy numbers. #include   <iostream> using   namespace   std ; int   power ( int   a ,  int   b ) {      int  result =  1 ;      for  ( int  i =  0 ; i < b; i++) {         result *= a;     }      return  result; } int   main () {      int  number, number2, cnt =  0 , digitnumber;     cout <<  "First 8 happy numbers are:"  << endl;      for  ( int  i =  1 ; cnt <  8 ; i++) {         number = i;          while  (number !=  89 ) {             digitnumber =