title: Modular arithmetic. How to solve the following equation?
body: <p>How to solve the following equation?</p>
  
  <p>I am interested in the methods of solutions.</p>
  
  <p><strong>n^3 mod P = (n+1)^3 mod P</strong></p>
  
  <p>P- Prime number</p>
  
  <p><strong>Short example</strong> with the answer. 
  Could you gives step-by-step solutions for my example.</p>
  
  <p><strong>n^3 mod 61 = (n + 1)^3 mod 61</strong></p>
  
  <p>Integer solutions:</p>
  
  <p>n = 61 m + 4,  </p>
  
  <p>n = 61 m + 56, </p>
  
  <p>m element Z</p>
  
  <p>Z - is set of integers.</p>