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After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy o£ its distinguished past. More and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods.
To be in a position to tackle these problems, it is necessary to be familiar with many specific aspects of number theory.
These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by studying and solving numerous problems. Now it is very easy to formulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible.
This is the objective realised by this work. It is the collaborative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
Without running through all the areas in number theory, which would have been excessive the exercises given here deal with those directions that now appear most important- The solutions are rarely easy, but this book always gives a method to solve them. The appearance of this volume is gratefully welcomed.
To all those who have made the effort to delve into the prob lems proposed here, it will solidify their attachment to the theory of numbers