Tarea_01.pdf
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Lista de Problemas de teor´ıa de n´ umeros 1.- Demostrar que 30 | n5 − n. 2.- Probar que si x y y son enteros impares, entonces x2 + y 2 es par, pero no es divisible entre 4. 3.- Probar que el cuadrado de cualquier entero es de la forma 3k o bien 3k + 1, pero no de la forma 3k + 2. 4.- Probar que si n es impar, entonces 8 | n2 − 1. 5.- Sean m, a, b enteros cualesquiera, probar que (ma, mb) = m · (a, b)
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