Speaking at a rally in New Hampshire on Jan. 5, Republican presidential candidate Donald Trump said that the voting system "is out of control" and alleged that people were voting "many, many times." (Reuters)

CLAREMONT, N.H. -- Donald Trump described voter fraud as a rampant problem during a rally on Tuesday night, even though the number of proven cases is minuscule.

"Look, you've got to have real security with the voting system," Trump said during a campaign event in western New Hampshire. "This voting system is out of control. You have people, in my opinion, that are voting many, many times. They don't want security, they don't want cards."

That brief comment came during a frenzied question-and-answer session at the end of an hour-long campaign rally in a high school gymnasium. There were no microphone as rally-goers shouted out questions, and Trump briefly answered them. At one point, he took a pause from this back-and-forth to take a selfie with a "good-looking guy" he invited onto the stage.

The first question came from a bellowing man who said some women in the military can't keep up with their male counterparts, posing a "serious risk," and asked if Trump would be willing to bar women from serving in the infantry.

"Isn't that a wonderful first question?" Trump said, as the crowd laughed. "I always get these easy questions the first time. Look: I'll tell you what, there is a tremendous amount of turmoil, as you know, going on in the military over that very issue."

Trump then polled the audience on the issue, finding the crowd mostly split although there seemed to be a few more people who supported women in the military. One woman shouted that women with children shouldn't be in the line of fire, and the man who asked the question kept shouting out things about "standards." Trump then said it's an issue that needs to continue to be debated.

Then came the second question from a woman in the audience: "I want to know: Do you believe in equal pay for women?"

"I do," Trump said. "I love equal pay. I love equal pay, I do. I mean, I have many women -- I was very, very forward, advanced on women. And, frankly, I have many, many women in my company who absolutely... I had a woman in charge of construction of a major tower in New York City 35 years ago, and that was unheard of. And I have many female executives and many of them are making actually more than the men for the same job. So, I mean, the men sometimes don't like me so much, to be honest with you. But I have found women to be absolutely amazing in the workplace. They've done a good job."

Then came a question about abuse of the welfare system, which Trump used as an opportunity to promise to save Social Security and Medicare unlike some of his Republican rivals.

"But you do have waste, fraud and abuse, and we're going to take care of that," Trump said. "It's a good question."

Trump then simultaneously answered questions about term limits and medical marijuana by saying: "Term limits are fine, term limits are fine. Medical, I do, medical is good, medical is good. Yes, go ahead, just shout them out."