' field below. // Please check man page for isset function. $submitted = isset($_GET['submitted']); if ($submitted) { $M0 = $_GET['n']; //I am putting the input number n into the variable $M0 $M1 = $_GET['d']; //writing d into M1 echo "

\$M0 = $M0 \$M1 = $M1

\n"; // copies the M0 content (n) in M2: $M2 = 0; // echo "

before: \$M2 = $M2 \$M0 = $M0

\n"; $M2 = $M2 + $M0; // echo "

after: \$M2 = $M2 \$M0 = $M0

"; // computes r = n - 4*[n/4] and puts the result into $M0: // echo "

0: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; $M2 = (int)($M2/$M1); // echo "

1: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; $M2 = $M2 * $M1; // echo "

2: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; $M0 = $M0 - $M2; // echo "

3: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; // if $M0 != 0 (i. e., r != 0) jumps to 14 if ($M0 != 0) { // echo "

flow 1: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; $M1 = 0; // writes 0 in $M1 if r != 0 and stops } else { // echo "

flow 2: \$M0 = $M0 \$M1 = $M1 \$M2 = $M2

\n"; $M1 = 0; // writes 1 in $M1 if r == 0 and stops $M1++; } echo "

the result: \$M1 = $M1

\n"; $dividend_n = $_GET['n']; $divisor_d = $_GET['d']; if ($divisor_d == 0) echo "

Be carefull !! d must not be 0.

\n"; else { if ($M1 == 0) echo "

$dividend_n is not a multiple of $divisor_d

"; if ($M1 != 0) echo "

$dividend_n is a multiple of $divisor_d

"; } echo '

recompute

'; } else { echo '

Theorem: Given any two Natural numbers n (dividend) and d (divisor) where d>0, there exists only one couple of natural nambers q (quotient) and r (reminder) such that n = q * d + r with r is less than d.

Program requrements: Given any two Natural numbers n and d with d>0 as input, the present program checks if n is a multiple of d (i. e., the reminder r above is equal to 0) or not.

n:

d:

'; } ?>