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copied!<p>The BigInteger class represents integers as immutable objects.</p> <p>There are two points here.</p> <ol> <li>Don't use <code>==</code> to test if two <code>BigInteger</code>s are equal</li> <li>To change the value of a BigInteger variable you must do <code>i = i.add(ONE);</code> and not just <code>i.add(ONE);</code>.</li> </ol> <p>The reason not to use <code>==</code> to compare <code>BigInteger</code>s is because instead of checking for numerical equality you are checking that they are the same object in memory.</p> <p>Consider with <code>String</code>s.</p> <pre><code>String a = "a"; String b = "b"; String x = a + b; String y = "ab"; </code></pre> <p>In the above example <code>x.equals(y)</code> is true because they contain the same number of characters in exactly the same order. However, <code>x == y</code> is not true because they are different objects in memory.</p> <p>The reason you need to to assign the result of arithmetic operations to a variable is because BigInteger is immutable. Thus arithmetic operations cannot change the value of the object it is operating on, but it can create a new BigInteger (which it returns). Which is why you must assign the result of the arithmetic operation to the variable you want it saved in.</p> <p>As an aside a shortcut for your lesserThanOrEqual to is this.</p> <pre><code>boolean result = m.compareTo(n) <= 0; </code></pre> <p>Basically </p> <ul> <li><code>m == n</code> becomes <code>m.compareTo(n) == 0</code></li> <li><code>m != n</code> becomes <code>m.compareTo(n) != 0</code></li> <li><code>m < n</code> becomes <code>m.compareTo(n) < 0</code></li> <li><code>m > n</code> becomes <code>m.compareTo(n) > 0</code></li> <li><code>m <= n</code> becomes <code>m.compareTo(n) <= 0</code></li> <li><code>m >= n</code> becomes <code>m.compareTo(n) >= 0</code></li> </ul>

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