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A reasonable number of problems with solutions on integer quadruples in A.P have been illustrated to enable the researchers to deepen their understanding of this subject and we hope that the creative readers may be motivated by the desire to achieve this goal. We hope the readers of this book may develop their ability to particularize and generalize, to pose and solve meaningful problems, to look for patterns and relations and to apply the logical thinking behind mathematical proof. Also, the researchers in this field may be encouraged to come out with diverse solutions to problems. No doubt that the wonders of numbers are numerous and amazing. It is worth to observe that true pleasure lies in the search for new problems. This book is concluded with the quotation by Erdos "I know numbers are beautiful. If they aren't beautiful nothing is". The real voyage of discovery consists not in seeing these problems but seeing with new eyes.
