Can exercise affect your periods?

Since you're on birth control pills suppressing ovulation you won't have "real" periods, the period of bleeding you'll have are called (monthly) withdrawal bleedings, meaning the womb's lining is shed during the period you're not taking pills containing the female sex hormone estrogen needed to support this lining. 
Women can defer this withdrawal bleeding for many months if the continue to take the hormone containing pill without a pause.
Some women won't have withdrawal bleedings in the week they don't take the hormone containing pills, this I think is what has happened to you.
Or are you on continuous hormonal active pills?
Even so, breakthrough bleedings do happen, usually during the first 6 months, less later on since the lining has thinned due to being on hormones for a long time.
Nothing to do with exercise.
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Calories play crucial role in weight loss. An average girl has to eat regarding 2000 calories per day to keep up, and 1500 calories to lose one pound of weight per week. a average man desires 2500 calories to keep up, and 2000 to lose one pound of weight per week. However, this relies on