Query a database containing all good abc triples whose c value is less than or equal to 108.

Query the database:

is the number

Display results as a single line.

" ; * */ /*Query the database! */ $query = "SELECT * FROM `abc` WHERE $condition "; $result = mysql_query($query); /*Display the results */ if ($_POST['singleline']) { while ($row = mysql_fetch_array($result,MYSQL_ASSOC)) { $aval = $row['avalue']; $bval = $row['bvalue']; $cval = $row['cvalue']; echo "($aval, $bval, $cval), "; } echo "
"; } else { while ($row = mysql_fetch_array($result,MYSQL_ASSOC)) { $aval = $row['avalue']; $bval = $row['bvalue']; $cval = $row['cvalue']; echo "($aval, $bval, $cval)
"; } } mysql_close(); } ?>

Definition of a Good abc Triple:

A good abc triple is a set of 3 positive integers a, b, c such that

  1. a + b = c
  2. gcd(a,b,c) = 1
  3. c > rad(abc)
where rad(n) is the product of all primes dividing n for n a positive integer.

The ratio of a good abc triple is simply log(c)/log(rad(abc)). A good abc example usually means a good abc triple whose ratio is greater than 1.4.

About the database:

The database contains all good abc triples with c value less than or equal to 108. The data is stored in a MySQL database and was generated using Python script files for SAGE.