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I checked the voltage at the battery before starting it was about 12.75V . While idling the battery voltage was 17.50 - 17.62 volts ( seems high to me ) .

I checked the voltage at the regulator at idle and it was 6.8-7.5 volts.
I checked the alternator at idle and it was about 7.8- 8.2 volts

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Double check your readings.

It is impossible to have 17.5 at the battery with 7.8-8.2 at the alternator.